We introduce a simple game family, called Constraint Logic,
where players reverse edges in a directed graph while satisfying
vertex in-flow constraints. This game family can be interpreted in
many different game-theoretic settings, ranging from zero-player
automata to a more economic setting of team multiplayer games
with hidden information. Each setting gives rise to a model of
computation that we show corresponds to a classic complexity class.
In this way we obtain a uniform framework for modeling various
complexities of computation as games. Most surprising among our
results is that a game with three players and a bounded amount
of state can simulate any (infinite) Turing computation,
making the game undecidable. Our framework also provides
a more graphical, less formulaic viewpoint of computation.
This graph model has been shown to be particularly appropriate for
reducing to many existing combinatorial games and puzzles—such as
Sokoban, Rush Hour, River Crossing, TipOver, the Warehouseman's Problem,
pushing blocks, hinged-dissection reconfiguration, Amazons, and Konane
(Hawaiian Checkers)—which have an intrinsically planar structure.
Our framework makes it substantially easier to prove completeness of
such games in their appropriate complexity classes.